Microwavable food trays are well known including designs by the inventor of the invention disclosed in this patent document. In one prior design by the inventor, disclosed in Publication No. WO 2007/056866, published May 24, 2007, an upper tray was loosely nested in a lower tray, with a gap between the trays to allow steam to vent from the lower tray during cooking. With such a design, however, steam escaping from the lower tray might burn a user's fingers when they picked up the upper tray. In another design, sold in Europe, and also mentioned in the Publication No. WO 2007/056866, snugly nested rectangular upper and lower trays provided separate compartments for different foods. This design, made of paperboard, was defective in that steam could build up between the snugly nested trays.